Several computational approaches have been introduced to reduce the breath-held duration in cardiac cine and to enable free-breathing imaging. Early approaches relied on carefully designed signal models to exploit the structure of the data in x-f space [1]}, [2]}, [3]}, sparsity [4]}, or binned the data to different phases [5]} which facilitates the signal recovery from undersampled measurements. In recent years, bilinear models[6]}, [7]}, [8]}, [9]}, which represent the signal as the product of spatial and temporal factors, have emerged as powerful alternatives for the recovery of large scale data. These adaptive approaches, where the signal model is learned from the data itself, are observed to be far more efficient than earlier strategies that relied on hand-crafted models. The factor-based framework has been combined with other priors, including low-rank and sparsity [8]}, [6]}, low-rank +sparse [12]}, blind compressed sensing that learns a dictionary from the data [13]}, and motion-compensation [14]}, [15]}. Recently, non-linear manifold models that rely on kernel low-rank relation have been shown to outperform the subspace-based models in the context of free-breathing and ungated cardiac MRI [16]}, [17]}, [18]}. Many of these schemes rely on k-space navigator measurements to estimate the temporal factors, while the spatial factors are estimated from the entire data. The kernel approach for estimating the temporal factors is observed to be more efficient in representing the dynamics, especially in free-breathing applications. A major benefit of the bilinear methods is the significantly reduced memory demand of these algorithms, in addition to the good reconstructions they offer. Specifically, the factors are significantly smaller in dimension than the dynamic dataset, which facilitates the recovery of large 3D volumes [19]}, [9]}. While early methods relied on calibration data to estimate one of the factors, the joint optimization of both the factors offers several advantages, including improved image quality [8]}, [13]}. The distinction between the methods can be viewed as the specific priors applied on the spatial and temporal factors, including energy priors in the low-rank setting [8]}, unit column norm and sparsity priors in the blind dictionary learning setting [13]}, and kernel priors in the manifold setting [16]}, [17]}.
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